Chapter 6

Learning Objectives

  • When you complete this supplement, you should be able to:

    • S6.1 Explain the purpose of a control chart.

    • S6.2 Explain the role of the central limit theorem in Statistical Process Control (SPC).

    • S6.3 Build x-bar and R-charts.

    • S6.4 List the five steps involved in building control charts.

    • S6.5 Build p-charts and c-charts.

Statistical Process Control (SPC)

  • Definition: Application of statistical techniques to ensure that processes meet standards.

  • Monitoring: A process used to monitor standards by taking measurements and taking corrective action while a product or service is being produced.

  • Objective: To provide a statistical signal when assignable causes of variation are present.

Process Variability

  • Types of Variability:

    • Natural (Common) Causes: Variability that is inherent in every process; affects practically all production processes; represents the expected amount of variation.

    • Probability Distribution: Output measures follow a probability distribution.

    • Special (Assignable) Causes: Variations that can be traced to specific reasons, generally representing changes in the process.

    • Objective: Discover when assignable causes are present, eliminate bad causes, and incorporate good causes.

Control Charts

  • Purpose: Constructed from historical data, aimed at distinguishing between natural variations and variations due to assignable causes.

  • Types of Control Charts:

    • Variable Control Charts: Characteristics that can take any real value (e.g., weight, length).

    • Attribute Control Charts: Used for categorical data (e.g., defective/non-defective).

    • Variable Control Charts: Designed for continuous data (e.g., measurements of time, temperature, size).

Sampling Distributions

  • Characteristics: The variability of the sampling distribution is less than that of the process distribution.

  • Effect of Sample Size on Distribution: As the sample size increases, the sampling distribution of means narrows, leading to less variability among sample means.

X-bar and R-Charts

  • X-bar charts: Used to monitor the mean of a process based on sample means.

  • R-charts: Monitor process variability by tracking the range in samples.

  • Control Limits for X-bar:

Five Steps in Building Control Charts

  1. Collect Samples: Collect 20 to 25 samples observed from a stable process and compute mean and range of each.

  2. Compute Control Limits: Set appropriate control limits, usually at the 99.73% level (3 sigma control limits).

  3. Graph Samples: Graph the sample means and ranges.

  4. Investigate Points: Check if points fall outside acceptable limits; if so, investigate for assignable causes.

  5. Revalidate Limits: Collect additional samples, if necessary, and revalidate control limits using new data.

Control Charts for Attributes

  • p-Charts: Used for tracking the fraction defective in categorized attributes; data follows a binomial distribution.

  • c-Charts: Count of defects in units of output, based on Poisson distribution; measures occurrences of defects.

Patterns in Control Charts

  • Run Tests: Identify if abnormalities exist; consider investigating for causes if:

    • One point is out of control.

    • A trend occurs where multiple points go upwards or downwards.

    • Patterns of points cluster near upper or lower control limits.

Managerial Issues with SPC

  • Key decisions managers must make:

    • Select points in the processes that require SPC monitoring.

    • Choose the appropriate charting technique.

    • Establish clear policies and procedures for SPC use.